Database of modular polynomials#

This module gives access to the database of modular polynomials. To use the database, you need to install the optional database_kohel package by the Sage command

sage -i database_kohel


sage: # optional - database_kohel
sage: DBMP = ClassicalModularPolynomialDatabase()
sage: f = DBMP[29]
sage: f.coefficient([28,28])


  • David Kohel (2006-08-04): initial version

class sage.databases.db_modular_polynomials.AtkinModularCorrespondenceDatabase#

Bases: ModularCorrespondenceDatabase

model = 'AtkCrr'#
class sage.databases.db_modular_polynomials.AtkinModularPolynomialDatabase#

Bases: ModularPolynomialDatabase

The database of modular polynomials Phi(x,j) for \(X_0(p)\), where x is a function on invariant under the Atkin-Lehner invariant, with pole of minimal order at infinity.

model = 'Atk'#
class sage.databases.db_modular_polynomials.ClassicalModularPolynomialDatabase#

Bases: ModularPolynomialDatabase

The database of classical modular polynomials, i.e. the polynomials Phi_N(X,Y) relating the j-functions j(q) and j(q^N).

model = 'Cls'#
class sage.databases.db_modular_polynomials.DedekindEtaModularCorrespondenceDatabase#

Bases: ModularCorrespondenceDatabase

The database of modular correspondences in \(X_0(p) \times X_0(p)\), where the model of the curves \(X_0(p) = \Bold{P}^1\) are specified by quotients of Dedekind’s eta function.

model = 'EtaCrr'#
class sage.databases.db_modular_polynomials.DedekindEtaModularPolynomialDatabase#

Bases: ModularPolynomialDatabase

The database of modular polynomials Phi_N(X,Y) relating a quotient of Dedekind eta functions, well-defined on X_0(N), relating x(q) and the j-function j(q).

model = 'Eta'#
class sage.databases.db_modular_polynomials.ModularCorrespondenceDatabase#

Bases: ModularPolynomialDatabase

class sage.databases.db_modular_polynomials.ModularPolynomialDatabase#

Bases: object